Question

Tìm số tự nhiên a, biết : 1/2×3 + 1/3×4 + 1/4×5 + ..+ 1/a×(a+1) = 49/100

Answer 1

Đặt \(A=\) \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{a\left(a+1\right)}=\frac{49}{100}\)

\(\Rightarrow A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{a}-\frac{1}{a+1}=\frac{49}{100}\)

\(\Rightarrow A=\frac{1}{2}-\frac{1}{a+1}=\frac{49}{100}\)

\(\)\(\Rightarrow\frac{1}{a+1}=\frac{1}{2}-\frac{49}{100}\)

\(\)\(\Rightarrow\frac{1}{a+1}=\frac{1}{100}\Rightarrow a+1=100\Rightarrow a=100-1\)

\(\Rightarrow a=99\)

                  Vậy \(a=99\)k cho mik nha :))